Planar depth and planar subalgebras

Landau, Zeph ; Sunder, V. S. (2002) Planar depth and planar subalgebras Journal of Functional Analysis, 195 (1). pp. 71-88. ISSN 0022-1236

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We consider the notion of planar depth of a planar algebra, viz., the smallest n for which the planar algebra is generated by its 'n-boxes'. We establish a simple result which yields a sufficient condition, in terms of the principal graph of the planar algebra, for the planar depth to be bounded by k. This suffices to determine the planar depth of the E6, E 8 and the 5+√13/2 subfactors. We then consider a planar subalgebra of the 'group planar algebra' which is naturally associated with a group θ of automorphisms of the given group G. We show that this planar algebra corresponds to the 'subgroup-subfactor' associated with the inclusion θ⊂(G⋊θ) (given by the semi-direct product extension). We conclude with a discussion of the planar depth of this planar algebra Pθ in some examples.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Operator Algebras; Subfactor; Planar Algebra; Standard Invariant
ID Code:53540
Deposited On:09 Aug 2011 11:52
Last Modified:09 Aug 2011 11:52

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